Vector 3-Component 3-Dimensional Kirchhoff Prestack Migration

ABSTRACT

An apparatus and a method for migration of three components, 3-Dimensions seismic (3-C, 3-D) data acquired by down-hole receivers and surface seismic sources. This method utilizes full 3 components reflection wave field. It uses a dynamic, vector energy mapping method to image a reflection position and maps each time sample only to its reflected image point. Therefore, this method reduces unwanted data smearing and false mirror images. This method overcomes the weakness of using only a single component trace or pre-rotated three-component traces in the 1-C or 3-C 3-D VSP migration and produces better 3-D image.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a divisional application of U.S. patent applicationSer. No. 10/972,880 filed on Oct. 25, 2004, now U.S. Pat. No. ______,which claimed priority from U.S. Provisional Patent Application Ser. No.60/515,107 filed on Oct. 28, 2003 and U.S. Provisional PatentApplication Ser. No. 60/576,526 filed on Jun. 3, 2004.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a method of geophysical prospecting whichimproves the accuracy of seismic migration. Specifically, the inventionuses offset or zero-offset survey measurements to accurately migratereflectors present in three-dimensional (3-D) surface seismic data, inVertical Seismic Profiles (VSPs), and in cross-well seismic survey data.

2. Description of the Related Art

In surface seismic exploration, energy imparted into the earth by aseismic source reflects from subsurface geophysical features and isrecorded by a multiplicity of receivers. This process is repeatednumerous times, using source and receiver configurations which mayeither form a line (2-D acquisition) or cover an area (3-D acquisition).The data which results is processed to produce an image of the reflectorusing a procedure known as migration.

Conventional reflection seismology utilizes surface sources andreceivers to detect reflections from subsurface impedance contrasts. Theobtained image often suffers in spatial accuracy, resolution andcoherence due to the long and complicated travel paths between source,reflector, and receiver. In particular, due to the two-way passage ofseismic signals through a highly absorptive near surface weathered layerwith a low, laterally varying velocity, subsurface images may be of poorquality. To overcome this difficulty, a technique commonly known asVertical Seismic Profiling (VSP) was developed to image the subsurfacein the vicinity of a borehole. In a VSP, a surface seismic source isused and signals were received at a downhole receiver or an array ofdownhole receivers. This is repeated for different depths of thereceiver (or receiver array). In offset VSP, a plurality of spaced apartsources are sequentially activated, enabling imaging of a larger rangeof distances than is possible with a single source.

The VSP data acquisition may be performed by conveying the receiversdownhole on a wireline after drilling of the well has been partially orfully completed. An advantage of the VSP method is that the data qualitycan be much better than in surface data acquisition. The VSP acquisitionmay also be done by conveying the receiver array downhole as part of thebottomhole assembly (BHA). This is referred to as VSP while drilling.

U.S. Pat. No. 4,627,036 to Wyatt et. al., the contents of which arefully incorporated herein by reference, gives an early example of theVSP method. Referring now to FIG. 1, there is illustrated a typical VSPconfiguration for land seismic acquisition. In the exemplary figures, aVibroseis® source 11 is illustrated as imparting energy into the earth.It is noted that any other suitable seismic source such as explosivescould be utilized if desired. In a marine environment, the source couldbe an airgun or a marine vibrator.

A receiver 12 is shown located at a desired depth in the borehole 14.For the location of the receiver 12, energy would be reflected from thesubsurface strata 15 at point 16. The output produced from receiver 12is recorded by the recording truck 17. In VSP, the receiver 12 wouldtypically be moved to a new location for each shot with the distancebetween geophone locations being some constant distance such as 50 feet.If desired, an array of receivers spaced apart by some desired distancecould be utilized or a plurality of sources spaced apart could be used.

Data obtained by VSP has the appearance of that illustrated in FIG. 2.Wyatt discusses the use of a processing technique called the VSP-CDPmethod by which VSP data such as those shown in FIG. 2 may be stacked toproduce an image of the subsurface of the earth away from the well.

The process of migration of surface seismic data has been used forobtaining images of the subsurface that are better then those obtainablewith the CDP or stacking method. In migration, the objective is toposition seismic reflections at their proper spatial position: in thesurface CDP method, on the other hand, it is assumed that reflectionsoriginate from a reflection point midway between the source and thereceiver. A commonly used method for migration is the Kirchhoff methodin which a velocity model is defined for the subsurface. Traveltimes arecomputed from the source to a diffraction point and from a diffractionpoint to the receiver. The actual image of a reflector is obtained bycombining data from a plurality of source-receiver pairs to a pluralityof imaging points. If the velocity model is reasonably accurate, thesignals will interfere constructively at the correct image point. Thisconcept was originally developed for surface seismic data. Wiggins(1984) extended the use of migration to cases where the observationsurface is not limited to being a flat horizontal plane. The use ofKirchhoff migration for VSP data has been discussed by Dillon.

The teachings of Dillon are limited to 2-D migration. More recently, VSPKirchhoff depth migration has been used for 3-D VSP data by Bicquart. Asnoted by Bicquart, Kirchhoff and other wide angle migration methods aresensitive to velocity error. Velocities are difficult to obtainaccurately in surface reflection seismology thus limiting theeffectiveness of Kirchhoff migration in structures associated with steepdips. In contrast to surface seismic acquisition, in VSP reasonablyaccurate velocities can be obtained accurately from the well survey.With good velocity depth information, Kirchhoff depth migration producesa better 3-D depth image in the well vicinity. However, in offset 2-DVSPand 3-DVSP source and receiver are not symmetric with respect to thesubsurface imaging points. This asymmetry requires considerable effortin computing weighting factors.

In parallel with the improvements in seismic data processing,particularly migration techniques, there has been continued developmentof a rather fundamental nature in the kind of data acquired. In recentyears, multicomponent seismic data has formed an increasing part of thetotal amount of seismic data acquired. The reason for this has been therecognition that conventional, single component seismic data isprimarily responsive to compressional wave energy in the verticaldirection in the subsurface. The conventional data is most commonlyacquired with a compressional wave source and hydrophone detectors in amarine environment, or a vertical source and a vertical detector in landseismic acquisition. Additional information indicative of lithology andfluid content of the subsurface is obtainable from knowledge about thepropagation of shear waves in the subsurface. Shear wave arrivals aremost conveniently detected by receivers with other orientations thanvertical. An additional advantage of multicomponent recording is that,even for compressional energy, knowledge of three components of areceived signal can provide an indication of the direction from whichenergy is received at the receiver, and total amount of energy in thatdirection.

Hokstad has derived equations for prestack multicomponent Kirchhoffmigration. The imaging equations are derived with basis in viscoelasticwave theory. The mathematical structure of the multicomponent imagingequation derived by Hokstad allows for computation of separate imagesfor all combinations of local incident and scattered wavemodes (qP-qP,qP-qS1, qS1-qS1, etc.).

A limitation of the teachings of Hokstad is that they do not address thereal world problem of 3-D seismic imaging. While the results derived byHokstad are quite elegant, the examples are limited to 2-D data and donot offer any practical suggestion of dealing with 3-D multicomponentdata. The problem of migration of 3-D multicomponent data is addressedin the present invention.

SUMMARY OF THE INVENTION

The present invention is a method of imaging subsurface earthformations. A seismic source is activated at one or more sourcepositions and seismic waves are generated into the earth formation.Three component (3-C) seismic data are obtained at one or more receiverpositions. The received seismic data contains information about the 3-Dstructure of the earth. A 3-D Kirchhoff migration of the 3-C data isdone. In the Kirchhoff migration, traveltimes from each source positionto a plurality of image points, and from each of the plurality of imagepoints to each of the receiver positions are used. The sources andreceivers may be at the surface or at a downhole location. Typically,the three components are substantially orthogonal to each other. In awireline implementation, the receivers for the three components may begimbal mounted. When used in a MWD environment, the receivers may bemounted on a non-rotating sleeve that can be clamped to the boreholewall. The receivers may be geophones or accelerometers.

The 3-D migration procedure includes forward modeling and imagingoperations. The forward modeling is to compute the seismic wavetraveltime and wave-(ray) direction angles at each image grid in the 3-Dspace within a proposed velocity model. These traveltime andray-direction angles are computed for each source and receiver location.The traveltimes may be for compressional waves or for shear waves.

The imaging operation sums the recorded reflected seismic wave energiesto their reflected locations using a weighting factor. The weightingfactor is a function of ray geometry, wave traveltime, source-receiveraperture, wavelet phase and other factors. The traveltimes are used tolocate the amplitude (reflected energy) in the recorded traces. Theoutput image amplitude of the migration is a scale value whichrepresents the geophysical reflectivity.

The imaging operations may be performed by an onsite processor.Alternatively, processing may be done at a time different from theacquisition at a remote location. Data from the wellsite may be sent tothe remote location by any suitable means, including a satellite link orby an Internet connection. The instructions enabling the processor toaccess the multicomponent seismic data and perform the 3C-3D migrationprocessing may reside on a machine readable memory device. Theseinstructions enable the processor to access the data and to process thedata.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is best understood by reference to the attachedfigures in which like numerals refer to like elements, and in which:

FIG. 1 (Prior Art) is a typical field geometry for the acquisition ofVSP seismic data;

FIG. 2 (prior art) is an illustration of actual VSP seismic data;

FIGS. 3 a and 3 b show a block diagram depicting operations carried outin one embodiment of the present invention;

FIG. 4 a displays a typical 3-C seismic data in x, y, z components;

FIG. 4 b is the data of FIG. 4A in a 3-D display;

FIG. 5 illustrates a drawback of the method of FIGS. 3 a and 3 b;

FIGS. 6 a and 6 b show a block diagram depicting operations carried outin a second embodiment of the present invention;

FIG. 7 a shows a synthetic survey model with one source and onereceiver;

FIG. 7 b shows synthetic 3-C traces for the model of FIG. 7 a;

FIGS. 8 a-8 c are 3D displays of the migrated image for the data in FIG.7 b using the conventional 3D migration method;

FIGS. 9 a-9 c are 3D displays of the migrated image for the data in FIG.7 b using the V3D migration method;

FIGS. 10 a-10 c show a comparison of results from a 2-D migration,conventional 3-D migration and the full vector 3-C, 3-D migration onfield data; and

FIG. 11 shows an example of a 3-C gimbal mounted 3-C receiver.

DETAILED DESCRIPTION OF THE INVENTION

For the present invention, a modified version of the prior art systemshown in FIG. 1 is used. The receiver 12 comprises an array of spacedapart receivers. Typically, 5-80 receivers are used. Each receivercomprises a three-component (3-C) receiver. In one embodiment of theinvention, the three components are labeled H1, H2 and Z components, theZ component being vertical, and the H1 and H2 axes are orthogonal to theZ axis and orthogonal each other. The receivers may be gimbal mounted.This facilitates use of the receivers in a deviated borehole. With suchan arrangement, the mechanical construction of the horizontal componentreceivers is usually different from the mechanical construction of the Zcomponent receiver due to the fact that the latter has gravity actingalong the direction of motion of the receivers. Either geophones oraccelerometers may be used. In an alternate embodiment of the invention,the three receivers are substantially identical in sensitivity and areoriented along the vertices of a tetrahedron. Orientation of thereceivers is determined using any of the methods known in prior art.

A basic part of the processing is the use of a 3-C 3-D vector Kirchhoffprestack migration. This is discussed prior to the implementation of themigration itself. The 3-D prestack Kirchhoff migration is generallyexpressed as

$\begin{matrix}{{M(x)} = {\sum\limits_{x_{s},x_{r}}{{W\left( {x_{s},x_{r},x} \right)}{P_{sr}\left( {{t_{s}\left( {x_{s},x} \right)} + {t_{r}\left( {x,x_{r}} \right)}} \right)}}}} & (1)\end{matrix}$

Here, M(x) is the migrated image point at 3-D location x. W(x_(s),x_(r), x) represents a weighting factor, or amplitude compensationfunction which relates to the survey geometry, velocities along theraypath, and the geophone aperture. x_(s) and x_(r) are the source andreceiver locations in 3-D. W(x_(s), x_(r), x) is independent of therecorded reflection wavefield P_(sr)(t_(s)(x_(s), x)+t_(r)(x, x_(r))),where t_(s)(x_(s), x) and t_(r)(x, x_(r)) are traveltimes from thesource to the image position and from the image position to thereceiver. The recorded wavefield P_(sr) is a superposition of scatteredenergy which satisfies the condition that recording time t=t_(s)(x_(s),x)+t_(r)(x, x_(r)) is constant for a source-receiver pair. The migrationprocess redistributes the recorded reflection energy at time t to anellipsoidal (in a constant velocity background, for simplicity) surfacewhere a reflector may exist. The migrated image at each position x is asuperposition of weighted energies WP_(sr) of all the ellipsoid surfacesat x for each source x_(s) to each receiver x_(r). The conventional 3-Dprestack Kirchhoff migration maps the energy at t non-directionally,meaning that the migration operator evenly distributes equal amplitudeto all points on the ellipsoid. As noted above, the conventionalKirchhoff migration does not take into consideration the direction fromwhich the energy as reflected from. This property will cause falsemirror image reflections to be produced. Using a vector term allows thevector 3-C, 3-D Kirchhoff migration to overcome this problem. Therecorded wavefield P_(sr) used in migration is a scalar one componentdata or rotated to a fixed direction of the three components data. Thetotal reflection wavefield is not used.

The vector 3-C, 3-D Kirchhoff prestack migration (V3D migration) isbased on the conventional Kirchhoff integration given by eq. (1). Theprincipal difference is the migration operator. The V3D migration treatsthe reflection wavefield at each time sample t as a 3-D wavefieldvector, rather than a scalar value as in conventional 3-D Kirchhoffmigration. An incoming ray vector (wave front normal) is introduced tothe equation. It is a unit vector which represents the ray direction atthe receiver from the reflected image point. When constructing the imageat location x using the wavefield P_(sr)(t_(s)(x_(s), x)+t_(r)(x,x_(r))), we use only the wavefield data which originated from x. Thedirectional information is determined using dynamic polarizationanalysis of the 3-component input data. Assuming that the reflectionwavefield vector at t is {right arrow over (P)}_(sr)(t) and the unit rayvector at location x_(r) is {right arrow over (R)}(x, x_(r)), then themigration equation (1) becomes

$\begin{matrix}{{{M(x)} = {\sum\limits_{x_{s},x_{r}}{{W\left( {x_{s},x_{r},x} \right)}{A\left( {x_{s},x_{r},x} \right)}}}},{where}} & (2) \\{{A\left( {x_{s},x_{r},x} \right)} = {{\overset{\rightarrow}{R}\left( {x,x_{r}} \right)} \cdot {{\overset{\rightarrow}{P}}_{sr}\left( {{t_{s}\left( {x_{s},x} \right)} + {t_{r}\left( {x,x_{r}} \right)}} \right)}}} & (3)\end{matrix}$

A(x_(s), X_(r), x) is the new migration operator. The weighing factorW(x_(s), x_(r), x) is unchanged.

Processing of the data is accomplished using a first embodiment of theinvention using equation (1) is illustrated in FIGS. 3 a and 3 b. The3-C seismic data are rotated to a pre-defined direction and becomes 1-Cdata or input any 1-C (mostly vertical component) data into themigration processing.

The 3-D traveltime tables for each source and receiver position aregenerated 101 using a velocity model for the subsurface. For one methoddiscussed with reference to FIGS. 3 a-3 b, the seismic data ispre-rotated into a direction generally corresponding to thereceiver-to-source direction 100. This may be referred to hereafter asthe conventional method. The travel time tables for each receiverposition are generated 103. For each 3-D spatial image location x,integrations of the amplitude with a weighting factor are carried outover all source-receiver pair. The amplitude is the trace value at thetotal travel time t=t_(s)(x_(s), x)+t_(r)(x, x_(r)) of eachsource-receiver pair. The weighting factor includes phase correction,ray trace geometry correction, source-receiver aperture correction, andother energy-lose related factors. The migrated image at each grid pointis the summation result of the above integrations 113 after allcontributions of the traces have done (109, 111).

The method of processing 3-C 3-D data discussed above has severaldrawbacks discussed next. First, the 3-C reflection data contains theenergy from all directions and comprises vectors at each recordingsample time at each receiver location in a 3-D space as shown in FIGS. 4a-b. Using single component data or rotating the data rotated in aspecified direction will eliminate the energy from all other directionsin the migration. This results in incomplete migration image. Secondly,algebraic summation of individual component migration results or usingalgebraically summed individual component data into the migration isincorrect. Thirdly, the received reflection energy is directional andshould be directionally distributed to its reflected direction. Equallydistributing the reflection energy in all azimuths will produce falsemirror images.

FIG. 5 shows the problem of false mirror images with the method ofprocessing shown in FIGS. 3 a-3 b. Shown in FIG. 5 is a plan view of a3-C, 3-D VSP acquisition geometry. The source is shown at 250 and thethree component receivers are depicted schematically by 221, 223 and225. Shown by 231 is a raypath for seismic energy that propagates fromthe source 250, is reflected at a true structure shown by 201 andtravels to the receivers 221, 223 and 225. With the method describedabove, assuming we use the reflection data from receiver component 221,the reflection energy is equally distributed to both location 201 and203. 203 is a false reflector. The reason is that the traveltime from250 to 201 and from 201 to 221 equals to the traveltime from 250 to 203and from 203 to 221. The energy distribution is non-directionally in theconventional first migration method. Similar results are obtained usingany rotated or un-rotated single component data.

To address the problem discussed above, a second embodiment of theinvention migrates the 3-C data in a vector form and rotate the 3-C datadynamically. This is shown in FIGS. 6 a-6 b. As in the first embodimentof the invention, data from a single shot are gathered and thecorresponding traveltime values t_(s)(x_(s), x) for this source areobtained 301 by forward modeling from the velocity model (or retrievingfrom memory). The traveltimes are obtained for each output location x inthe 3-D volume. Next, the traveltime values are obtained t_(r)(x, x_(r))303 for a selected receiver location to the grid of desired output imagepoints x in the 3-D volume. For each image grid location point x, thetotal traveltime from the source to the receiver is t=t_(s)(x_(s),x)+t_(r)(x, x_(r)). Three component amplitudes are obtained for thesetraces at t 307. The 3-C data are rotated to the image-to-receiverray-direction 309. It is, of course, necessary to keep in mind that theray direction usually corresponds to the direction of maximum amplitudefor a P-wave, whereas for shear waves, the ray direction will usually beorthogonal to the direction of maximum amplitude. Amplitude and phasecorrections are applied to the trace and the product is added to theimage grid 311. Not shown in FIG. 6 a but implicit in the Kirchhoffmigration is that the processing is done for a plurality of image pointson an image grid.

A check is made to see if there are more traces. If so, the process goesback to 303. If there are no more traces for this particular sourceposition, a check is made to see if there are more source positions 315.If there are more source positions, processing goes back to 301. Ifthere are no more source positions, the migrated image is output 317.Additional modes are then processed using substantially the samemethodology.

The methodology discussed above may be implemented taking into accountanisotropy in the velocity fields for the compressional and shear waves.The traveltime computation then is done using the anisotropicvelocities.

More discussions of ray directions and the particle motion directions isgiven, for example, in a classic paper by Postma. One embodiment of thepresent invention performs the 3-C, 3-D imaging for transverselyisotropic media. A slightly more complicated situation arises whenazimuthal anisotropy (due to stress or fracturing) is superimposed on aTI medium. For such a medium, the elastic tensor has orthorhombicsymmetry. The most general types of earth formations have morecomplicated elastic tensors. While in theory it is possible to doraytracing through such media, (see, for example, Crampin) formulationof the elastic tensor is problematic.

The method of the present invention has been discussed above withreference to data acquired in a VSP survey. In theory, the method couldalso be used with data recorded at the surface.

To illustrate the advantages of V3D migration over conventional 1-C, 3-DKirchhoff prestack migration, we examine the impulse response of therecorded wavelet. For simplicity, a single source-receiver pair is usedin a constant background velocity model shown in FIG. 7 c. The recordeddata consists of two 3-component wavelets, one at 1 sec and the other at2 sec. To clearly illustrate the directional effect of the migration,sample amplitudes of the recorded wavelets are only in x-direction at 1second and are only in y-direction at 2 seconds as shown in FIG. 7 c.This corresponds to reflectors in the x-direction and y-directionrespectively. Conventional, pre-rotated 3-C or 1-C data migration ofthese traces result in one or two ellipsoidal surfaces, depending uponon how the data is rotated prior to migration. In any case, theamplitude of each ellipsoidal surface will have constant amplitude. Thisis of course due to the non-directional distribution of the data in theconventional 3-D migration. The energy is evenly distributed to allellipsoidal surface points that satisfy the travel time condition forthat sample. FIGS. 8 a, b and c show the migrated images of the 3Dcross-section displays in the x and y directions using the pre-rotateddata in the maximum energy direction. The image amplitudes are identicalin x and y sections. The polarities of the amplitude are symmetric tothe receiver location which means the energy mapping is non-directional.The source and receiver positions are indicated by 501 and 503.

Utilizing the full 3-component data, the migrated image from V3Dmigration is different. For the wavelet at 1 sec, the amplitude of themigrated image reaches a maximum in the x direction and is zero in the ydirection For the wavelet at 2 sec, the amplitude reaches its maximum inthe y direction and is zero in the x direction. See FIGS. 9 a-c. The V3Dmigration produces a reversed polarity image in the opposite directionto the receiver location from the positive image. This is correctbecause that reflection response of a reflector with a positivereflectivity in one direction of the receiver is identical to theresponse of a reflector with a negative reflectivity in a reverseddirection to the receiver. A conventional 3-D migration will generatesame polarity images along the entire ellipse.

Results from a field example are shown in FIGS. 10 a-10 c. FIG. 10 a isthe 2-D migration in the source-receiver plane of conventional 2-D dataacquired in the vicinity of a salt dome. The 2-D migrated image ismerely a 2-D projection of the 3-D reflections to the source-receiverprofile. The image in FIG. 10 b was obtained from the 3-C, 3-D VSPKirchhoff migration using the data which were pre-rotated to the maximumenergy (the first method discussed above). The migration results for the3-D salt image do not correctly resolve the off-line salt reflection;the salt image is positioned symmetric to the source-receiver line. Thisis due to the fact that the non-directional mapping of the reflectiondata in conventional 3-D migration does not map data to only itsoriginal location. It maps the reflection energy symmetrically.Migrating the 3-C data with the vector 3-C, 3-D VSP migration shows alateral variation of the salt body normal to the source-receiver line(FIG. 10 c), consistent with the current geologic interpretation.

The method of the present invention has been discussed with reference toa VSP survey carried out on a receiver assembly conveyed on a wireline.However, this is not a limitation on the method of the presentinvention. The method of the present invention can also be carried outusing three component receivers conveyed on a bottomhole assembly (BHA)and surface seismic processing.

Reference has been made to gimbal mounted receivers. An example of agimbal mounted receiver is shown in FIG. 9 where three sensors 701, 703,705 are gimbal mounted in an inclined housing 707. The sensor 701 isable to maintain a vertical orientation even though the housing isinclined. Such a configuration is necessary in order to get threecomponents of the seismic field in a fixed reference coordinate system.Orientation of the housing within the borehole may be determined bysuitable orientation sensors such as magnetometers.

Baker Hughes Incorporated has a multi-level receiver (MLR) that can beconfigured from 1 to 13 levels. This greatly speeds up the dataacquisition. The downhole receivers can be run in combination with otherlogging services, either wireline or pipe-conveyed, reducing the numberof trips into the well and saving rig time. In high-angle wells, thedownhole receiver can be conveyed on drill pipe or coiled tubing andalso run in combination with a variety of openhole logging servicesgreatly reducing rig time.

The 3C-3D vector migration methodology described above may beimplemented on a general purpose digital computer. As would be known tothose versed in the art, instructions for the computer reside on amachine readable memory device such as ROMs, EPROMs, EAROMs, FlashMemories and Optical disks. These may be part of the computer or may belinked to the computer by suitable communication channels, and may beeven at a remote location. Similarly, multicomponent seismic data of thetype discussed above may be stored on the computer or may be linkedthrough suitable communication channels to the computer. Thecommunication channels may include the Internet, enabling a user toaccess data from one remote location and get the instructions fromanother remote location to process the data. The instructions on themachine readable memory device enable the computer to access themulticomponent data and process the data according to the methoddescribed above.

While the foregoing disclosure is directed to the preferred embodimentsof the invention, various modifications will be apparent to thoseskilled in the art. It is intended that all such variations within thescope and spirit of the appended claims be embraced by the foregoingdisclosure.

1. A system configured to evaluate an earth formation, the systemcomprising: a seismic source at least one source position configured togenerate seismic waves into the earth formation, at least one receiverconfigured to receive three components of seismic data at a plurality ofreceiver positions the at least one source position and the plurality ofreceiver positions defining a plurality of source-receiver combinations;and a processor configured to: (i) use a vector combination of the threecomponents of the seismic data to define a contribution from each of theplurality of source-receiver combinations to an amplitude of an image ata plurality of image points using traveltimes from the at least onesource position to the plurality of image points and traveltimes fromthe plurality of image points to the plurality of receiver positions;(ii) combine, at each of the plurality of image points, thecontributions to the amplitude from each of the plurality ofsource-receiver combinations to produce an image of the earth formation.2. The system of claim 1 wherein the at least one source position is atleast one of (i) a surface location, and (ii) a downhole location. 3.The system of claim 1 wherein the three components of seismic data aresubstantially orthogonal to each other.
 4. The system of claim 1 whereinat least one of the plurality of image points is part of a reflectinginterface.
 5. The system of claim 1 wherein the processor is furtherconfigured to use a velocity model for obtaining the traveltimes.
 6. Thesystem of claim 1 wherein the seismic waves by the seismic sourcecomprise at least one of: (i) compressional waves, and, (ii) shearwaves.
 7. The system of claim 1 wherein a portion of the seismic datareceived by the at least one receiver corresponds to at least one of:(i) a compressional wave, and, (ii) a shear wave.
 8. The system of claim1 wherein the processor is further configured to process the threecomponents of seismic data by further rotating the three components ofthe received seismic data in a specified direction.
 9. The system ofclaim 1 the processor is further configured to use the vectorcombination of the three components of seismic data by further rotatinga vector sum of the three components of the seismic data in a specifieddirection.
 10. The system of claim 8 wherein the specified direction isin a vertical plane passing through the at least one source position.11. The system of claim 8 wherein the specified direction is defined bya line joining at least one of the plurality of image points to at leastone of the plurality of receiver positions.
 12. The system of claim 9wherein the specified direction is in a vertical plane passing throughthe at least one source position and the at least one of the pluralityof receiver positions.
 13. The system of claim 9 wherein the specifieddirection is defined by a line joining at least one of the plurality ofimage points to at least one of the plurality of receiver positions. 14.The system of claim 1 wherein the plurality of image points are on agrid of output points.
 15. The system of claim 1 wherein the processoris configured to define the contribution by further applying acorrection that is at least one of: (i) an amplitude correction, and,(ii) a phase correction.
 16. The system of claim 1 wherein the at leastone source position further comprises a plurality of additional sourcepositions.
 17. The system of claim 15 wherein the at least one sourceposition further comprises a plurality of additional source positions.